minimum_variance.py

import matplotlib.pyplot as plt
import numpy as np
import csv


def yahoo_finance_close_chart(filename, label=None):
    with open(filename) as f:
        reader = csv.reader(f, delimiter=",", doublequote=True,
                            lineterminator="\r\n", quotechar='"', skipinitialspace=True)
        rows = [row for row in reader]
        rows = rows[1:]
        series = [float(row[4]) for row in rows]

        returns = []
        for i in range(len(series)):
            if i != 0:
                returns.append(np.log(series[i] / series[i - 1]))
        return returns


def correlation(xs, ys):
   return np.corrcoef(np.array([xs, ys]))[0][1]

spy = yahoo_finance_close_chart('./SPY.csv', 'SPY')
tlt = yahoo_finance_close_chart('./TLT.csv', 'TLT')

assert(len(tlt) == len(spy))

"""
xs = []
ys = []
co = []
for i in range(len(tlt)):
    if i != 0 and i % 100 == 0:
        co.append(correlation(xs, ys))
        xs = []
        ys = []
    xs.append(spy[i])
    ys.append(tlt[i])
"""

# SPY のみ
co = []
xs = []
for i in range(len(tlt)):
    if i != 0 and i % 20 == 0:
        co.append(np.std(xs))
        xs = []
    xs.append(spy[i]) # * 0.5 + tlt[i] * 0.5)

# SPY と TLT が5割5割
co2 = []
xs = []
for i in range(len(tlt)):
    if i != 0 and i % 20 == 0:
        co2.append(np.std(xs))
        xs = []
    xs.append(spy[i] * 0.5 + tlt[i] * 0.5)


# TLT のみ
co3 = []
xs = []
for i in range(len(tlt)):
    if i != 0 and i % 20 == 0:
        co3.append(np.std(xs))
        xs = []
    xs.append(tlt[i])


# 今月の分散が最小になるように今月の比率を決める (現実には不可能)
co4 = []
xss = []
for r in range(101):
    xss.append([])
for i in range(len(tlt)):
    if i != 0 and i % 20 == 0:
        co4.append(min([ np.std(xs) for xs in xss ]))
        xss = []
        for r in range(101):
            xss.append([])
    for r in range(101):
        xss[r].append(spy[i] * r / 100 + tlt[i] * (1 - r / 100))


# 今月の分散が最小になるように次の月の比率を決める
co5 = []
xss = []
for r in range(101):
    xss.append([])
nextr = 50
for i in range(len(tlt)):
    if i != 0 and i % 20 == 0:
        stds = [ np.std(xs) for xs in xss ]
        co5.append(stds[nextr])
        for r in range(101):
            stds[r]
            if stds[r] < stds[nextr]:
                nextr = r
        xss = []
        for r in range(101):
            xss.append([])
    for r in range(101):
        xss[r].append(spy[i] * r / 100 + tlt[i] * (1 - r / 100))


plt.plot(co, label="SPY : TLT = 10 : 0")
plt.plot(co2, label="SPY : TLT = 5 : 5")
plt.plot(co3, label="SPY : TLT = 0 : 10")
plt.plot(co4, label="minimum variance weight by this month (impossible)")
plt.plot(co5, label="minimum variance weight by previous month")
plt.legend()
plt.show()